when I had my 243 handi, I had to limit my number of reloads to about 3, so I would get 4 total shots out of each one. I think the more necked down the cartridge is, the harder it is on brass. I think there is too much pressurized frontal area has to be held back by the lockup mechanism and any bit of poor fitup is quickly exposed. Hence, I have abandoned my 243 and 25-06 in the handi rifles.
And 4 layers of clear office tape (what is called scotch tape) sounds like too much, when I switch/reinstall savage barrels, I only buy a go gage and use 2 layers of tape on it to mimic a nogo gage. With the bolt guns, I can close hard on one layer and not close the bolt on 2 layers.